Problem: Simplify the following expression: $k = \dfrac{-7x^2 + 63x - 126}{x - 6} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $-7$ , so we can rewrite the expression: $ k =\dfrac{-7(x^2 - 9x + 18)}{x - 6} $ Then we factor the remaining polynomial: $x^2 {-9}x + {18} $ ${-6} {-3} = {-9}$ ${-6} \times {-3} = {18}$ $ (x {-6}) (x {-3}) $ This gives us a factored expression: $\dfrac{-7(x {-6}) (x {-3})}{x - 6}$ We can divide the numerator and denominator by $(x + 6)$ on condition that $x \neq 6$ Therefore $k = -7(x - 3); x \neq 6$